Course Profile Mathematics for Everyday Life (MEL4E), Grade 12, Workplace Preparation, Combined
Unit 6: By Design
Time: 22 hours
Activity
6.1 | Activity 6.2 | Activity 6.3 | Activity 6.4
| Activity 6.5 | Activity
6.6 | Activity 6.7
Unit Description
Students apply their
understanding of measurement and geometry to two-dimensional and
three-dimensional constructions and symmetrical designs. Drawing software is
used to create two-dimensional scale drawings and three-dimensional drawings of
a room. Spreadsheet software is used to plan and evaluate project costs in a
household improvement. Students are provided class time to apply their
understanding of scale to the construction of a 3-D scale model of an area of
personal interest such as a garden or bridge. The geometric properties of
tiling designs and logos are investigated using drawing software and concrete
materials. Students complete these investigations with the construction of a
personal logo and tiling designs. The summative activity provides an
opportunity for students to demonstrate their understanding of the
decision-making processes involved in planning, designing, and costing a
household improvement.
Unit Synopsis Chart
|
Activity/ Time |
Learning Expectations |
Assessment Categories |
Tasks |
|
1 7.5 |
AMV.02, AM2.09 |
Knowledge/Understanding |
Design a household
improvement. |
|
2 2.5 |
AMV.02, AM2.05,
AM2.06 |
Knowledge/Understanding |
Construct scale
drawings using technology. |
|
3 3.75 |
AMV.02, AM2.07 |
Application |
Design and build
3-D scale models. |
|
4 1.25 |
AMV.03, AM3.01 |
Knowledge/Understanding |
Analyse
symmetrical designs using technology. |
|
5 1.25 |
AMV.03, AM3.02,
AM3.03 |
Knowledge/Understanding |
Construct a
personal logo using technology. |
|
6 3.75 |
AMV.03, AM3.04,
AM3.05 |
Thinking/Inquiry/Problem
Solving |
Apply tiling
principles to the construction of tiling designs with technology. |
|
7 1.25 |
AMV.02, AMV.03,
AM2.05, AM2.09, AM3.02, AM3.05 |
Knowledge/Understanding |
Making design and
purchase decisions. |
Note: 0.75 hours have been allotted for introducing
the Transform menu on Geometer’s Sketchpad.
Activity
6.1: Upgrade your Space
Time: 7.5 hours
Description
Students plan and
design a household improvement and calculate project costs within a given
budget. A field trip to a home improvement centre is included to acquaint
student with the variety of decisions that are made regarding product choices,
label reading, and pricing when planning a project. In addition, the visit
provides an opportunity for students to demonstrate and strengthen workplace
skills such as showing initiative to address job-site challenges and organizing
their time efficiently.
Strand(s) & Learning Expectations
Ontario Catholic
School Graduate Expectations
CGE4f - a
self-directed, responsible, life-long learner who applies effective
communication, decision-making, problem-solving, time and resource management
skills.
Strand(s): Applications of Measurement and Geometry
Overall
Expectations
AMV.02 - solve
problems involving measurement and design.
Specific
Expectations
AM2.09 - investigate
the making of a household improvement, design the improvement, and estimate and
calculate the cost, using technology.
Prior Knowledge & Skills
·
Calculate
perimeter and area using a calculator.
·
Measure and read
metric and imperial measures; determine an appropriate scale and construct
scale drawings using drawing software.
·
Calculate costs
using unit prices.
Planning Notes
·
Book the computer
lab or provide access to classroom computers.
·
Provide
calculators, pencils, building supply flyers, home renovation magazines and
books.
·
Bring a home
improvement supply such as paint cans for label reading practice to class.
·
Prepare sample
worksheets.
·
Prepare and
install the spreadsheet on the computers.
·
Make prior
arrangements with the home improvement store for a tour on the day of the store
visit. Book buses and prepare permission forms as required or prepare a list of
on-line catalogues in order to access product availability, pricing, and label
information.
·
Task 2 must be
completed after Activity 2. This provides time to revise the project, take
measurements, and learn to draw 2-D scale drawings using technology.
Teaching/Learning Strategies
Teacher
Facilitation
Task
1: Project Proposal
·
Provide a budget
amount, for example, $250 and record in Sample Worksheet 1.
·
Brainstorm
project ideas with the students and record them on chart paper. Guide students
so that project plans are reasonable in size and depth and within the budget
amount. For instance: painting, wallpapering, and adding decorative moulding is
reasonable but changing the interior structure of a room or adding an addition
is beyond the expectations of this activity.
·
Review the 6
tasks and determine due dates and record them on Sample Worksheet 1.
·
In preparation
for the scale drawings in Task 2, students must measure the floors and walls
(if painting or carpeting a floor for example) or decide on the dimensions of
the project (if constructing a bookcase or a cedar chest for example) and bring
the measurements to class.
·
Review the rubric
that will be used to evaluate the project.
Task
2: Scale Drawings
·
Complete this
task after students have constructed 2-D scale drawings in Activity 2.
·
Tell students to
identify and label all objects that are part of the upgrade on the scale
drawing.
Task
3: Supply List
·
Provide store
flyers for material selection and to determine the quantity of supplies
required for the project.
·
Demonstrate how
to fill in the supply list using an example from the flyers or a package.
Students use the flyers to complete any sections of the supply list they can.
Tell them that coverage data will be collected during the store visit. Check to
ensure that lists are complete.
·
Demonstrate
appropriate label reading prior to the store visit using a paint can as an
example.
Task
4: Store Visit
·
Ensure that
students have brought the supply list in Sample Worksheet 2, clipboards, and
pencils.
·
Provide
assistance reading labels for coverage and completing the price column of the
supply list. In most cases the quantity will be calculated in Task 5.
·
Ensure that the
Supply, Label Information and Unit Price columns of the Supply List are
complete before leaving the store.
Task
5: Project Costs
·
Review method of
calculating the amount of supplies required using label information and
calculating costs using unit price with an example. For instance: Calculate the
number of cans of paint needed to paint a classroom wall using the label
information; then, demonstrate how the unit price can be used to calculate the
total paint costs. Model the ways spreadsheets or calculators can be used to
calculate both the quantity and supply costs. Post these instructions for
student reference.
·
Ensure that
calculations are adjusted so that students are purchasing full packages, cans
of paint, etc.
·
Assist students
as they adjust their material list in order to stay within their budget.
Task
6: Evaluating/Presenting
·
Discuss the
reflection and presentation prompts in Sample Worksheet 4
Student Activity
Students:
The project consists
of six 75-minute tasks: a project proposal; a scale diagram using technology; a
supply list; a store visit; the calculation of project costs; project
evaluation/presentation.
Task
1: Project Proposal
·
Review household
improvement magazines and books and decide on a project to investigate such as
redecorating a room, tiling a floor, building a bookcase, refinishing furniture.
·
Complete the
project proposal in Sample Worksheet 1.
Sample Worksheet 1
Project Proposal
Describe your
project:
Draw a sketch of
your project:
You will complete
your project during class time. We have agreed on the following due dates:
1. Proposal ______________
2. Scale Drawing __________ (Bring measurements
to class on this date.)
3. Supply List/ Quantity_____
4. Field Trip (Store Visit)____
5. Project Costs___________
6. Presentation____________
Budget amount: ___________
Signed: _____________________(Student)_______________________(Teacher)
Task
2: Scale Drawing
·
Construct a scale
drawing of the project using GSP or by hand.
Task
3: Supply List
·
Determine which
supplies are needed to construct the project (including gloves, drop cloths,
etc.) and complete the supply list in Sample Worksheet 2.
Sample Worksheet 2
(Expand this Supply List to include more rows)
|
Supply |
Quantity |
Label information (Coverage) |
Unit Price |
|
|
|
|
|
·
Determine the
quantity required using the information in the flyers and formulas, (i.e.,
area, perimeter) or spreadsheets with formulas if the information is available
in the flyer.
Task
4: Store Visit
·
Students complete
the label information and price section of the supply list.
·
Students collect
samples, e.g., paint chips, wallpaper, if desired for the presentation.
Task
5: Project Costs
·
Calculate the
Quantity column in the Supply List using the Label Information column.
·
Estimate project
costs using the Quantity column and Unit Price in the supply list.
· Enter the estimate in the spreadsheet in Sample Worksheet 3 then calculate total project costs.
· Review project costs and make adjustments in order to stay within the budget.
Sample Worksheet 3
(Expand to include more rows)
|
|
A |
B |
C |
D |
E |
|
1 |
Supply |
Quantity |
Unit Price |
Project Costs |
Estimate: |
|
2 |
|
|
|
=B2 *C2 |
|
|
3 |
|
|
|
|
|
|
4 |
|
|
Sub Total |
=SUM(D2:D3) |
|
|
|
|
|
Taxes |
=D4*.15 |
|
|
|
|
|
Total |
=D4 + D5 |
Budget Amount: |
Task
6: Project Evaluation/Presentation
·
Collect and
organize completed worksheets and prepare to present the proposal.
·
Reflect on the
work and present the proposal using the prompts in Sample Worksheet 4.
Sample Worksheet 4
|
Reflecting on
my work |
Presenting my
Project |
|
I am proud of… |
My project was
about… |
|
I need to get
better at…. |
Some choices I had
to make were… |
|
Next time I would… |
The cost of the
project was over/under the budget. I had to… |
Assessment & Evaluation of
Student Achievement
Students require formative feedback on the
reasonableness of their project proposal prior to the construction of scale
drawings. Assess the project cost calculations and the accuracy of their scale
drawings under Knowledge/Understanding. The decision-making required to stay
within the budget can be evaluated under Problem Solving. The degree of clarity
in their project presentation could be assessed under Communication. The selection
of an appropriate scale and using it to construct a scale drawing can be
assessed under Application.
Accommodations
Allow students to
provide verbal descriptions or use point form.
Resources
http://www.cmhc.ca/banner1/
provides project ideas.
http://www.rona.ca/
provides on-line home improvement catalogues.
Home
Improvement Store flyers.
Readers Digest, New
Complete Do-It-Yourself Manual. Montreal: Readers Digest Canada 1991.
ISBN: 0888501781
Activity
6.2: Make Room!
Time: 1.5 hours
Description
Students measure the
classroom, choose an appropriate scale, and construct a two-dimensional scale
drawing of the room using Geometer’s Sketchpad (GSP). A
three-dimensional drawing of the interior is created with drawing or design
software.
Strand(s) & Learning Expectations
Ontario Catholic
School Graduate Expectations
CGE4b - a
self-directed, responsible, life-long learner who demonstrates flexibility and
adaptability.
Strand(s): Applications of Measurement
and Geometry
Overall
Expectations
AMV.02 - solve
problems involving measurement and design.
Specific
Expectations
AM2.05 - make a
two-dimensional scale drawing of a room, using design, or drawing software
effectively;
AM2.06 - create a
three-dimensional drawing of the interior of a room, using design or drawing
software effectively.
Prior Knowledge & Skills
·
Students must
know how to construct lines and use the measure and graph menus on GSP.
Planning Notes
·
Book the computer
lab or provide access to classroom computers with drawing software.
·
Set the distance
units to centimetres or inches and the precision to tenths if using GSP.
·
Students require
rulers, calculators, metric, and imperial measuring tapes, grid and plain
paper.
·
Provide 2-D
metric and imperial scale drawings such as maps and floor plans and 3-D
drawings.
·
Prepare Sample
Worksheets.
Teaching/Learning Strategies
Teacher
Facilitation
·
Lead a
whole-class discussion, using familiar examples of scale drawings in two
dimensions. For each example students discuss why scale diagrams are useful,
why the scale is appropriate, and how the scale is used to determine the
measurements in the diagrams.
·
Facilitate the
completion of the practice exercises in Sample Worksheet 1 by making reference
to the scales used in maps and floor plans and constructing a scale drawing as
an example.
·
Engage students
in a whole-class discussion about choosing an appropriate scale for the
classroom. There will be more than one appropriate scale. Model the use of both
metric and imperial scale units with examples drawn on chart grid paper. Review
Sample Worksheet 2, Part One. Check grid paper scale drawings to ensure that
the measurements and scale are accurate.
·
Demonstrate how
to use the GSP instructions in Sample Worksheet 2 Part Two with an example.
·
Provide time to
complete the reconstruction of the scale drawing.
·
Demonstrate the
construction of the 3-D drawing of the room. More than one strategy should be
provided so that students can make an informed choice. One way to begin is with
a grid-paper scale drawing of a wall. Students cut out the drawing and trace it
once to form one wall then slide the template left or right and trace again to
draw the opposite wall. Connecting the corners of the two templates creates the
third dimension. Another strategy uses one-point perspective to construct the
second wall.
·
Both GSP and
Paint can be used to reproduce either of these 3-D construction
techniques. Demonstrate both technologies so that students can make an informed
choice.
Student Activity
·
Measure the
classroom and create a scale drawing of the classroom using grid paper.
·
Recreate the
scale drawing using drawing software and print the drawing.
·
Create a
three-dimensional drawing of the interior using drawing software.
Sample Worksheet 1
(Expand to include more examples)
|
Resource |
Scale |
Real Measurement |
Scale Measurement |
|
|
100:1 |
15 m |
|
|
|
|
8 feet |
1 inch |
1. Measure 2 objects in the classroom, e.g.,
textbook, desk, computer screen.
2. Sketch and label a diagram of the objects you
measured.
3. Decide on an appropriate scale and explain
why you made this choice.
3. Using grid paper, make a scale drawing of the
object.
4. Label the sides with the actual measurements.
Sample Worksheet 2:
Scale Drawing of a Room
Part One: Measure the room and calculate the scale
measurements.
1. Draw a sketch of the perimeter of the floor
of the classroom.
2. Measure the perimeter and height of the
classroom. Label the sketch and complete the table.
3. Add the measurements for the two objects you
measured in Sample Worksheet 1.
4. Determine an appropriate scale. Use the scale
to complete the table:
|
Scale: |
Real Measurements |
Scale Measurements |
|
Classroom length |
|
|
|
Classroom width |
|
|
|
Classroom height |
|
|
5. Using grid paper make a scale drawing of the
room.
Part
Two:
Reconstruct the scale drawing. (The following instructions use GSP)
1. Create the grid paper: Select Graph: Show
Grid and Hide Axes.
2. Create the corners: Place points at a grid
mark close to the 4 corners in the paper scale drawing.
3. Construct a rectangle: Holding the shift key,
select the points. Select Construct: Segment.
4. Measure the sides: Holding the shift key,
select the sides in order. Select Measure: Length.
5. Adjust the measurements: Select Graph: Hide
Grid. Select a corner and drag until the measurements display accurate scale
lengths. Repeat as required then Select Graph: Show Grid.
Assessment & Evaluation of
Student Achievement
Formative assessment
of the knowledge required to choose an appropriate scale for the classroom can
be made to provide feedback to students prior to the construction of the scale
drawing of the home improvement project in Task 2 of Activity 1.
Accommodations
Students could
construct rectangular rooms. Provide access to scripts for rectangles if using GSP
to construct the 2-D and 3-D drawings. Allow students to submit the grid
paper scale drawings.
Resources
Paint (Windows 95/98 drawing program), Geometer’s
Sketchpad or other drawing software.
TABS+ 3-D
Modeling is a design and modeling software suitable for these constructions.
http://www.nycenet.edu/oit/math-kitecture/index.htm
provides instructional ideas for scale drawings.
http://mathforum.org/workshops/sum98/participants/sanders/
gives three-dimensional drawing ideas.
Activity
6.3: Objects are Larger than They
Appear
Time: 3.75
hours
Description
Students design and
construct a 3-D scale model of an area of personal interest such as a bridge,
garden, or cabinet. The model construction is divided into four parts. First,
students select work groups by interest and plan the model by preparing
sketches of all views. An appropriate scale is determined and scale conversions
are calculated and applied to the construction of a prototype in the second
part. In the third part modelling materials are applied to the prototype in
order to provide structural reinforcement and decorative design. Students
complete the activity with a project reflection that assesses application of
measurement skills and teamwork.
Strand(s) & Learning Expectations
Ontario Catholic
School Graduate Expectations
CGE5a - a
collaborative contributor who works effectively as an interdependent team
member.
Strand(s): Applications of Measurement and Geometry
Overall
Expectations
AMV.02 - solve
problems involving measurement and design.
Specific
Expectations
AM2.07 - construct,
with reasonable accuracy, a scale model of an environment of personal interest.
Prior Knowledge & Skills
·
Students must be
able to use the metric system.
Planning Notes
·
Provide 3-D
models such as cars, trains, and bridges with the scale indicated.
·
Provide scaled
objects such as nested boxes, rectangular and trapezoidal prisms.
·
Students will
work in small groups.
·
Provide access to
one computer per group with a spreadsheet program to calculate the scaled
dimensions installed.
·
Provide rulers,
tape measurers, metre sticks, and 1 cm grid paper.
·
Prepare Sample
Worksheet 1.
·
Provide suitable
model building materials such as popsicle sticks, foam board, Bristol board,
markers, pencils, glue, tape, glue gun, and scissors.
Teaching/Learning Strategies
Teacher
Facilitation
Day One:
·
View 3-D models
and discuss the choice of scale.
·
Brainstorm ideas
for models such as bridges, gardens or cabinets and sketch students’ choices in
3-D onto chart paper (Use a separate sheet of chart paper for each model
building idea). Evaluate the reasonableness of each model idea in light of the
timelines for the activity and revise accordingly.
·
Discuss
approximate “real” measurements of the dimensions for these objects and add
this information to the chart paper. Students choose their project by
proceeding to the sheet of chart paper model ideas according to their interest.
Direct each group member to complete Sample Worksheet 1 Part One and remind
students to bring any measurements they may require to class the next day.
·
Demonstrate how
to plan the model construction using a filing cabinet (or similar classroom
object) as an example. Following the outline in Sample Worksheet 1 Part Two,
sketch all views of the cabinet (front, back, sides, top), measure, and label
the dimensions. Provide concrete strategies for determining an appropriate
scale. One strategy that encourages students to decide on the size of the model
and then calculate the scale is as follows: Measure the largest dimension on
the filing cabinet (e.g., height = 108 cm). Using their hands, students gesture
the size the height will be on the model (e.g., 20 cm). This measurement will
be the scaled length. Using a spreadsheet with formulas, show students how to
determine the remaining scaled dimensions for the model. A spreadsheet is
provided below however the calculations can be done effectively without a
spreadsheet.
|
|
A |
B |
C |
|
1 |
Dimension to be
scaled |
Real Dimension |
Scaled Dimension |
|
2 |
Cabinet Height |
108 |
20 |
|
3 |
|
any real
dimension |
=C2 * B3 / B2 |
·
Record the scale
dimensions beside the real measurements on the sketch.
·
Provide time for
students to practise choosing a scale and calculating the scaled dimensions
using either a table or spreadsheet by completing Sample Worksheet 2.
Day Two:
·
Review scale
calculations using a table or spreadsheet by referencing the previous day’s
filing cabinet calculations and the practice calculations in Sample Worksheet
2.
·
Review Sample
Worksheet 1 Part Two. As students complete the worksheet, check the object
views, the real dimensions, choice of scale, and calculations for accuracy.
·
Demonstrate the
construction of a grid-paper prototype using the filing cabinet scale
calculations and sketches from the previous day. Create and cut out all grid
templates and show how Bristol board will provide stability by gluing it on to
the front of the model.
·
Students should
begin constructing the prototype when the scale dimensions are completed.
Day Three:
·
Monitor students
and provide assistance with model construction challenges.
·
Prompt students
to be specific when completing Part four of Sample Worksheet 1.
Student Activity
Students complete
Sample Worksheet 1 which requires that they:
·
select a model
project and group members by interest;
·
sketch the model,
record real dimensions, and determine an appropriate scale for the model;
·
calculate the
scale measurements and construct a prototype;
·
complete a
project reflection.
Sample Worksheet 1
(Expand to provide room for the sketches)
Part
One:
Planning the Model
Group Members:
Sketch:
Teacher Check__
Part
Two:
Choosing an Appropriate Scale for the Model
1. Sketch all the views of the object (front,
back, sides, top, bottom) and label with the actual dimensions:
Teacher Check__
2. Where is the largest dimension? ___________.
How long is it? ________________
3. How many 1-cm grid squares would you like
this to be on your model? _______________
4. Enter these numbers in a table or
spreadsheet. Calculate the length of all the model dimensions.
5. Place the scale dimensions beside the actual
dimensions on all the views sketched in Part Two.
Teacher Check__
Part
Three: Building
a Grid-Paper Prototype and Constructing the Model
1. Using the scale dimensions, count grid
squares to create a template for each surface.
2. Cut out the templates and label: front/back,
left side/right side.
3. Hold the templates in place to check how your
model will look. Adjust as necessary.
Teacher Check__
4. Glue Bristol board to the front of the grid templates.
5. Colour the exterior to represent the original
object.
6. Assemble the surfaces with glue.
Part
Four:
Reflecting on your Work
|
I am proud of… |
Next time, I will… |
|
My group helped
me…. |
I helped the group
by… |
Sample Worksheet 2
|
A Television has the following dimensions:
|
1. Where is the largest length in the model? 2. How many grid squares will you represent
this length in the model? 3. Calculate the scale dimensions of the
television and add them to the sketch. |
Assessment & Evaluation of
Student Achievement
Application can be
assessed with the appropriateness of the choice of scale for the model and
student’s ability to apply it accurately to all dimensions in the completed
model. Teamwork can be assessed by observing students as they work in groups to
solve design and construction challenges and by assessing the project
reflection in Sample Worksheet 1 Part Four.
Accommodations
Provide samples of different nets for the models. Allow students to describe or tell about the model. Allow students to use TABS+ software.
Resources
www.scalemodel.net/
– provides a list of scale model sites and related information.
Activity
6.4: Signs of Symmetry
Time: 1.25
hours
Description
The activity uses a
cooperative learning strategy called Jigsaw to teach students how to create
symmetrical patterns using the Transform menu on GSP. Expert groups
learn to construct one of the transformations (translation, reflection,
rotation, dilatation) and return to their home groups to teach the skill to
their group members. Students apply these skills to a cooperative
reconstruction of a logo.
Strand(s) & Learning Expectations
Ontario Catholic
School Graduate Expectations
CGE4b - a
self-directed, responsible, life-long learner who demonstrates flexibility and
adaptability;
CGE5a - a
collaborative contributor who works effectively as an interdependent team
member.
Strand(s): Applications of Measurement and Geometry
Overall
Expectations
AMV.03 - apply
transformation geometry in creating effective designs.
Specific
Expectations
AM3.01 - describe
the use of translations, reflection, rotation, and dilatations as they relate
to symmetry and design in logos, with the aid of technology.
Prior Knowledge & Skills
·
Students have
previous experience using Geometer’s Sketchpad in the Grade 9
Mathematics courses.
Planning Notes
·
Book the computer
lab or have classroom computers available.
·
Prepare Appendix
6.4.1 – Symmetry; one copy per group
·
Provide access to
Escher art that demonstrates the use of transformations to create designs.
·
Students work in
groups of 4 (called home groups).
·
Construct
Appendix 6.4.2 – Learn to Draw Course using GSP on computers and prepare
instructions; one per computer.
·
Post GSP instructions
for the Transform menu.
·
Construct
Appendix 6.4.3 – Transformations using GSP on computers.
·
Laminate the logo
in Appendix 6.4.4 – Logo; one copy per group and construct the logo template in
Appendix 6.4.4 – Logo on computers.
·
Jigsaw is a
cooperative learning strategy. Students form small groups (home groups). Each
group member meets with one member from each of the other home groups to form
an expert group. The expert group learns and practises one skill until they are
experts. (Expert means that they would be able to explain and demonstrate the
skill to someone else). Once they are experts this group returns to meet with
their home group members to teach them what they have learned. In this way
students learn many skills, and work cooperatively to complete a larger or more
complex task than might be possible in a similar amount of time.
Teaching/Learning Strategies
Teacher
Facilitation
·
Introduce the
terminology and physical motions associated with symmetrical pattern making through
an activity with the home group as explained below.
·
Distribute
envelopes containing a template shape for making symmetrical patterns, a sheet
of symmetrical patterns made with the shape, and names and descriptions of the
symmetry to each group (A suggestion is found in Appendix 6.4.1 – Symmetry).
Direct student groups to match the template with the symmetrical pattern and
the name of the transformation that created the pattern. It is important for
students to connect the name (slide, flip, turn, enlarge/reduce) with the
motion that created the pattern. Suggest that students move the template across
the patterns, adjusting the position and orientation of the shape in order to
make a match. In this way the students make a physical connection between the pattern
and the symmetry name. Encourage the groups to describe the physical motion
they used to recreate the design.
·
Discuss the
application of the above transformations in the Escher art samples.
·
The next part of
the activity uses jigsaw to teach students how to use the Transform menu to
create these transformations. Home groups are directed to send one person to
each of the four computer “stations” where the GSP instructions outlined
in Appendix 6.4.3 - Transformations using GSP have been installed. Two or
three computers may be required at each “station” in order to accommodate two
students per computer. Tell students that they will learn how to use one of the
GSP symmetry tools (flip, slide, turn, rotate, enlarge/reduce) at their
“station” and practise it by constructing the transformations they created
concretely until they become “experts” with the tools.
·
Direct students
to move into their jig saw positions. Once they are assembled at the computers
explain that students will need to take a short Learn to Draw course.
·
Direct students
to open the file in Appendix 6.4.2 – Learn to Draw Course. Students follow the
prompts in their jigsaw groups to learn to use the point, segment, and arrow
keys in GSP. Once completed, the students should be able to follow the GSP
directions in Appendix 6.4.3 – Transformations using GSP.
·
Demonstrate the
use of the symmetry tools in Appendix 6.4.3 – Transformations using GSP to the
whole class using a Computer/TV monitor hook up. The direction lines for
slides, the mirror lines for flips, the rotation points and enlarge/reduce
points will work when you activate them. Begin with the shape used at the start
of the activity. Demonstrate the slide, flip, rotation, and enlarge/reduce.
Model the sequence of steps: Mark the line or point using the tool under the
Transform menu; Select the shape; Choose the transformation under Transform
following the prompts provided in
Appendix 6.4.3 – Transformations using GSP.
·
Direct students
to begin work with their expert group. Remind students that experts are able to
teach someone else their skill by explaining and demonstrating how the tool
works. Provide sufficient time for students to become experts.
·
Monitor the
“stations” providing assistance and clarification when necessary.
·
After about 20 minutes
students should return to their home groups and “teach” the rest of the group
by demonstrating the transformation skills using the shapes in Appendix 6.4.3 –
Transformations using GSP in addition to shapes that students construct
themselves. Help students remain focused by providing them with a recording
sheet on which they make notes on the four transformations.
·
Distribute a
laminated copy of the logo in Appendix 6.4.4 – Logo, to each the home groups
once all students have demonstrated how to construct slides, flips, and turns,
and enlarge/reduce. Discuss the use of slides, flips, turns, and dilatations in
this logo.
·
Direct students
to open the file containing the logo template. The logo contains the four
skills that were learned in the expert groups and shared with other students.
Students should share the construction of the complete logo exchanging
positions at the computer when their skill is required. Students should save
the logo reconstruction using an appropriate file name.
Student Activity
·
Describe the use
of flips, slides, turns, and enlargement/reduction in patterns using
technology.
·
reconstruct a
logo using the Transform menu on GSP.
Assessment & Evaluation of
Student Achievement
Formative assessment
of Knowledge/Understanding of transformations can be made by asking students to
describe the transformations in the Escher art or in the logo reconstructions.
Communication can be assessed with a peer assessment checklist as students
teach each other in the home groups. The completion of the logo reconstruction
in a given time frame can be assessed under Organization.
Accommodations
Allow students to
construct the GSP tasks in Appendix 6.4.3 – Transformations using GSP
using concrete materials such as templates of the GSP shapes.
Students may submit a concrete logo reconstruction using templates for tracing
onto grid paper. Reinforce instructions with visual prompts or individually.
Resources
For an
on-line explanation of transformations and examples of symmetry go to:
http://www.schools.ash.org.au/stkierans-manly/Classes/Yr6/6B/Symmetry/page1.html
Gibbs, J. Tribes:
A new way of Learning Together. Concord: Irwin Publishing, 1994.
ISBN 0-7725-2118-2
Activity
6.5: Personal Logo
Time: 1.25
hours
Description
Students apply their
understanding of transformations to the analysis of symmetrical designs and the
construction of a personal logo using Geometer’s Sketchpad.
Strand(s) & Learning Expectations
Ontario Catholic
School Graduate Expectations
CGE3c - a reflective
and creative thinker who thinks reflectively and creatively to evaluate
situations and solve problems.
Strand(s): Applications of Measurement and Geometry
Overall
Expectations
AMV.03 - apply
transformation geometry in creating effective designs.
Specific
Expectations
AM3.02 - analyse the
geometric aspects of interesting and appealing applications;
AM3.03 - create a
personal logo, using the mathematics of symmetry, translations, reflections,
rotations, or dilations, with the aid of technology.
Prior Knowledge & Skills
·
Students must
know how to construct symmetrical patterns using the transform menu on GSP and
identify the sequence of transformations used to create symmetric patterns.
Planning Notes
·
Collect and
laminate a set of symmetry resources for each group of four students. Each set
should include a variety of the following: wallpaper, logos, quilt patterns,
and carpet designs sorted by complexity.
·
Provide access to
the computer lab or classroom computers.
·
Prepare the
Sample Worksheet.
·
Provide access to
written and “visual” instructions for the Transform menu.
Teaching/Learning Strategies
Teacher
Facilitation
·
Introduce the
activity with an examination of symmetry resources posted in the classroom.
Encourage students to identify the key features of these designs based on
polygon shapes. They are to incorporate the four transformations and may
reflect a cultural motif (carpet, pottery and tile designs), personal style, or
product message (personal and business logos).
·
Distribute a set
of laminated symmetry resources to groups of four students.
·
Distribute the
Sample Worksheet and indicate that students are to analyse two symmetrical
designs, one of which should be a logo.
Sample Worksheet 1
Attach
a symmetric design and a logo and answer the following questions for each:
1. The logo has reflection symmetry if you can
flip one half of the design onto the other. (Y/N)
2. The logo has translation symmetry if you can
slide one part of the design onto itself. (Y/N)
3. The logo has rotational symmetry if you can
turn the design onto itself at least once. (Y/N)
4. The logo uses dilatations if one part of the
design was enlarged or reduced. (Y/N)
· Model the completion of the worksheet using a sample design. Tell students that the designs are sorted by complexity. Provide time for students to complete this worksheet.
· Engage students in a whole-class discussion about the features of the logos they analysed in the worksheet and the purpose of a logo (advertise a product, make a personal statement) in order to provide ideas for their own logo. Using a polygon and for alphabet letters, create a personal symbol.
· Remind students that the patterns they constructed in Activity 6.4 have provided them with some ideas with which to begin their own logo: turns can used to create rosettes; letters can be created with flips and borders can be created with slides.
· Review the rubric in Appendix 6.5.1 – Rubric for Transformations, with the students. Clarify with the students that their evaluation will be based on their knowledge of the transformation tools, the application of these tools to create an effective design, and a description of how the logo was created using appropriate vocabulary.
· Direct students to move to the computers and begin their logo construction. Students should construct their logo with a grid displayed. Select Graph: Show Grid and Hide Axes.
Student Activity
·
Analyse the
geometric aspects of one symmetrical design and one logo.
·
Construct a
personal logo which demonstrates the application of at least three of the
transformation techniques and conveys a personal message.
·
Present the logo
to the whole class and describe the transformations using the statements in the
Sample Worksheet as a guide.
Assessment & Evaluation of
Student Achievement
A rubric to assess
this activity is provided in Appendix 6.5.1. Knowledge/Understanding can be
assessed by examining the skill with which they create symmetrical shapes using
the Transform menu by selecting “Show all Hidden” under Display. Application
can be assessed with the selection and coordination of the symmetry tools to
create an effective logo design. Communication can be assessed through their
description of how they designed the logo.
Accommodations
Provide access to
partial constructions or templates that provide students with a way to start
should they request it. Students may construct the logo with concrete
materials.
Resources
http://www.gopromos.com/idea_center/stock_art_alpha.asp?type=L
– provides access to corporate logos.
http://www2.spsu.edu/math/tile/index.htm
– provides a selection of cultural designs.
http://155.187.10.12/flags/flags.html
– displays flags of the world.
www.style-line.com
– analyses the symmetry in hubcaps.
http://mathforum.com/geometry/rugs/
– examines the symmetrical designs in rugs.
Activity
6.6: Tiles R Us
Time: 3.75
hours
Description
Students begin the
activity with a whole class investigation to determine the characteristics of
shapes that tile. These exploratory concrete experiences introduce students to
the geometric problem solving that they will encounter when they construct
tiling designs. Students apply and extend these geometric skills through the
construction of two tiling designs using paper templates and technology. An
emphasis is placed on using tactile, concrete materials in order that students
solve these geometric problems through physical movement. A variety of
technologies, requiring various skill levels, are provided as both construction
tools and to enhance designs.
Strand(s) & Learning Expectations
Ontario Catholic
School Graduate Expectations
CGE4f - a self-directed,
responsible, life-long learner who applies effective communication,
decision-making, problem-solving, time and resource management skills;
CGE5h - a
collaborative contributor who applies skills for employability,
self-employment, and entrepreneurship relative to Christian vocation.
Strand(s): Applications of Measurement and Geometry
Overall
Expectations
AMV.03 - apply
transformation geometry in creating effective designs.
Specific
Expectations
AM3.04 - determine,
through investigations, using concrete materials and technology, the
characteristics of shapes that will tile the plane;
AM3.05 - create
designs involving tiling patterns, using technology.
Prior
Knowledge & Skills
·
Experience with
the Transform Menu and the left hand Toolbox is required in order to select,
rotate, and drag objects on the screen if GSP is used for tiling. CorelDraw
5 is an efficient alternative that does not require a sophisticated
sequencing of tools and procedures.
·
Experience with
the Paint program will simplify the construction of Escher-like Art.
Planning
Notes
·
Book the computer
lab or provide classroom computers with Paint, CorelDraw 5 and GSP installed.
·
Construct the
shapes in Sample Worksheet 2 on the computers using both Geometer’s
Sketchpad and Corel Draw 5 and laminate card stock templates of
these shapes (a few of each one so they can be shared) in a size that is
suitable for tracing and creating paper and pencil designs.
·
Gather and post
tiling designs such as quilts, interlocking bricks, Escher art, and ceramic
tiles.
·
Provide a set of
pattern blocks (10-15 of each block) for every four students.
·
Prepare the
technology instructions in Appendix 6.6.1 – Tiling Instructions.
·
Prepare Sample
Worksheets.
·
Prepare sets of
four index cards with the following pictures: 1 of 4 different triangles, 1 of
4 different quadrilaterals, etc., in sufficient number to provide one card per
student to be used to form groups.
·
Provide cardstock
paper for constructing the Escher-like tiling templates.
·
Provide 8
× 11 blank paper, pencils, coloured pencils, scissors,
card-stock paper, and tape.
Teaching/Learning
Strategies
Teacher
Facilitation
·
Introduce the
activity with discussion about the features of tiling designs using ceramic
tiles, Escher art, and interlocking bricks as examples. Prompt student
discussion with guiding questions that encourage students to consider the
common features of all the designs: no gaps or overlaps, and repeating patterns
of one or many shapes that cover the entire surface.
·
Record the
characteristics of tiling patterns on chart paper and post within the room.
·
Arrange students
in groups of four using a strategy that involves matching polygons of the same
kind (see Planning Notes) and provide each group with a set of patterns blocks.
·
Instruct students
to make patterns with their blocks leaving no gaps or overlaps. When completed,
encourage them to share the results with the whole class, rotating around the
room as they observe each other’s work and share design plans. Prompt student
discussions with questions such as: Which shapes fit together easily? Which
shapes don’t fit together? Which shapes will make patterns by themselves?
·
Distribute Sample
Worksheet 1 and review the activity with the students. This activity is an
extension of the exploratory activity just completed as a whole class. It is
suggested that group members divide the investigations among themselves in
order that they benefit from multiple experiences. These experiences prepare
students for the types of geometric problem-solving that will be required to
complete the tiling designs in Sample Worksheets 2 and 3. Encourage students to
use trial and error and to consider many combinations. It is a challenge to
create tilings with just two or three different blocks. Assist students who are
having difficulty by suggesting a way to start. Share results and review and
reinforce the concepts that were learned. Refer to the tiling resources that
were viewed at the beginning of the activity and ask students to consider
questions such as: What other tile shapes might create tiling designs? Do you
think you have to use polygons?
·
Use this
discussion to introduce the last part of the activity during which students
create tilings using two methods: tracing templates and using Escher drawing
techniques.
·
Divide the
grouped students into two large groups for the remainder of the activity.
·
Distribute Sample
Worksheets 2 and 3 to both groups and review the expectations: In Sample
Worksheet 2 students choose a template of a shape from List 1 or List 2 and create
a tiling design by tracing it on to paper. Tell students that the shapes in
List 1 create designs using translations (easy) whereas the shapes in List 2
require a combination of rotations and translations (challenging). Students
create a tiling design using one of the templates and demonstrate the
reconstruction of the design with GSP using the instructions in Appendix
6.6.1 – Tiling Instructions, or CorelDraw 5 as an example. Tilings that
use a shape from List 2 require previous experience and skill with the rotation
tool on GSP. CorelDraw is an effective and appropriate
alternative. Demonstrate the technology by constructing a tiling design using GSP
and CorelDraw 5.
·
In Sample
Worksheet 3 students create an Escher-like template and trace it to create a
free-form tiling design. Students begin with a cardstock rectangle and create a
free-form template by cutting and rearranging the cut out pieces. Create a
tiling design by constructing a template and demonstrate the reconstruction of
the design with Paint as an example.
·
Tell students
that one of the groups will start with Sample Worksheet 2 and the other group
will start with Sample Worksheet 3. They will switch to the other Worksheet
part way.
Students Activity
·
Determine the
characteristics of shapes that tile using pattern blocks through the
investigations outlined in Sample Worksheet 1.
·
Create tiling
designs using concrete materials and technology as outlined in Sample
Worksheets 2 and 3 using the technology guides provided in Appendix 6.6.1 –
Tiling Instructions.
Sample Worksheet 1
Part
One: Tiling
Designs that Use One Pattern Block
1. Choose one pattern block and trace the
outline here:
2. Trace the pattern blocks chosen by the
members of your group:
3. Select 10 more of your block. Create a tiling
pattern.
4. Look at the tiling designs created by your
group members. Which ones tile?…don’t tile?
Part
Two: Tiling
Designs that Use Two Pattern Blocks
1. Choose two different pattern blocks and trace
their outline here:
2. Trace the pattern blocks chosen by the
members of your group:
3. Select 10 more of each of these blocks.
Create a tiling pattern.
4. Look at the tiling designs created by your
group members. Which ones tile?…don’t tile?
Part
Three: Tiling
Designs that Use Three Pattern Blocks
1. Choose three different pattern blocks and
trace the outline here:
2. Trace the pattern blocks chosen by the
members of your group:
3. Select 10 more of your block. Create a tiling
pattern.
4. Look at the tiling designs created by your
group members. Which ones tile?…don’t tile?
Sample Worksheet 2:
Students draw a tiling design using a laminated template
|
|
1. Choose a laminated template
of a shape from List One or List Two. 2. Trace the template onto a
sheet of paper. 3. Reposition the template next
to the traced outline. Trace the outline. Repeat until the page is filled. 4. Colour the design. 5. Reconstruct the paper and
pencil design using either GSP or CorelDraw 5 6. Save and print your design. |
Sample worksheet 3: How to create an Escher-like template
|
Create a paper
template: |
|
Create a template
with the Paint Activity program: |
|
Draw an altered
edge on the left side of the rectangle. |
|
Select the Free
Form Select Tool: Draw a line through the top and bottom at back to the
start. |
|
Cut along the
line. Slide to the other side. Tape edges. |
|
Click and drag the
cut out to the opposite side of the rectangle. |
|
Repeat the above
steps on the upper edge. |
|
Repeat the above
steps on the upper edge and position the cut piece on the lower side. |
|
Trace and
reposition the template to create a tiling pattern. Add colour and details. |
|
Select the
Scissors Tool: Draw a rectangle around the figure and copy it. Drag the copy
away from the original and colour it. Repeat the above to tile the area. |
Assessment & Evaluation of
Student Achievement
Assess the student’s
ability to select and sequence appropriate transformations to reconstruct the
tiling design using technology under Problem Solving.
Resources
Lee, Kevin. TesselMania,
1995 is a computer program that constructs tiling designs easily.
For information about Escher art
and constructing tilings – http://library.thinkquest.org/16661/ Once at the site, select Totally
Tessellations, An Introduction to Tessellations
and http://www.izzy.net/~jc/EscherTiles/EscherTiles.html
Activity
6.7: Summative Activity: All Tiled Up!
Time: 1.25
hours
Description
Using a case
scenario, students construct a tiling design and investigate the costs of a
flooring project using drawing software and spreadsheet technology. A proposal
that includes a scale drawing, a tiling design, project costs and an analysis
of the budget is submitted for evaluation.
Strand(s) & Learning Expectations
Ontario Catholic
School Graduate Expectations
CGE5h - a
collaborative contributor who applies skills for employability, self-employment
and entrepreneurship relative to a Christian vocation.
Strand(s): Applications of Measurement and Geometry
Overall Expectations
AMV.02 - solve
problems involving measurement and design;
AMV.03 - apply
transformation geometry in creating effective designs.
Specific
Expectations
AM2.05 - make a
two-dimensional scale drawing of a room, using design, or drawing software
effectively;
AM2.09 - investigate
the making of a household improvement, design the improvement, and estimate and
calculate the cost, using technology;
AM3.02 - describe
the geometric aspects of interesting and appealing applications;
AM3.05 - create
designs involving tiling patterns, using technology.
Prior Knowledge & Skills
·
It is expected
that students know how to construct a scale drawing and tiling designs using GSP.
Planning Notes
·
Book the computer
lab or provide classroom computers.
·
Construct the
tiles for the case scenario using drawing software.
·
Install the
spreadsheet in Sample Worksheet 1 on the computers.
·
Prepare the case
scenario in Sample Worksheet 2.
Teaching/Learning Strategies
Teacher
Facilitation
·
Ensure that
students have access to their work from Activities 6.1 to 6.6.
·
Distribute and
read the case scenario. Review the function of the materials in the supply list
and clarify the directions: they may create a design with one or both tiles and
their evaluation will consider the complexity of this choice. Tiles are boxed
by any selection of pieces. Students should calculate the number of boxes
required based on the floor area only, not the area of the individual tiles.
·
Demonstrate the
use of the spreadsheet in Sample Worksheet 1 at the computers.
Student Activity
Complete a
case scenario and submit a disc or printed documents for evaluation.
·
Draw a room to
scale using drawing software.
·
Construct a
tiling design using drawing software.
·
Estimate and
calculate project costs for a tiled surface and a vinyl flooring surface.
·
Prepare a
purchase recommendation based on an analysis of the flooring options and the
budget.
Sample Worksheet 1: Expand this spreadsheet to provide more rows
|
|
A |
B |
C |
D |
|
1 |
Total tiled area |
(enter total
area) |
Number of boxes of
tiles |
= B1/.8 |
|
2 |
Tiling Supplies |
Quantity |
Unit Price |
Cost |
|
3 |
|
|
|
|
|
4 |
|
|
|
|
|
5 |
|
|
Subtotal |
=SUM(D3:D4) |
|
6 |
|
|
Tax (GST/PST) |
=.15*D5 |
|
7 |
|
|
Total Project
Costs |
=D5+D6 |
Sample Worksheet 2: Case Scenario
|
A homeowner plans
to upgrade an entrance hall. While removing the baseboard and flooring
materials, an old tiled floor was discovered. At the present time the
homeowner must decide whether to replace the tile with vinyl flooring or
restore the old tiled surface. $150 has been budgeted for the upgrade but the
homeowner would consider exceeding the budget slightly. A sketch of the
hallway, tiles and a supply list is provided below. Complete a proposal for
this project. Your proposal must include:
|
|||
|
Supply List |
|
|
|
|
Supply |
Coverage |
Price |
Notes |
|
Tiles |
0.8 m2* |
$22.50/box |
*A box contains an
assortment of tiles |
|
Vinyl flooring |
1.8 m x 2.7 m |
$84.00plus
$25.00** |
** The cost of
levelling the sub-floor. This is required in order to keep the 5-year
guarantee. |
|
Tile adhesive: |
1.3 m2/L |
$11.95/7.6L pail |
|
|
Tile grout |
3 m2/box |
$10.95/box |
|
|
Vinyl adhesive |
70 m2/pail |
$10.99/3.8L pail |
|
|
Trowel |
NA |
$3.86 |
|
|
gloves |
NA |
$5.00 |
|
|
cleaning solutions
|
4L |
$11.99 |
|
Assessment & Evaluation of
Student Achievement
· A rubric is provided in Appendix 6.7.1 – Sample Rubric. Knowledge/Understanding can be assessed though the choice of scale, the calculations, and the construction of the scale drawing. Application can be assessed by examining the student’s ability to use the spreadsheet to evaluate project costs and make a purchase recommendation. Problem Solving can be evaluated through the analysis and justification of the purchase recommendation and though the selection of the tools required to create a tiling design. Communication can be evaluated by the clarity of the arguments given in the purchase recommendation.
Accommodations
· Provide scripts for rectangles and allow students to construct the design with concrete materials. Allow students to verbally present their analysis of the budget.
Appendix 6.4.1
Symmetry
|
|
Create and cut
out the name and definition strips below. Make a template of the shape to the
left in a size suitable for tracing the patterns below. |
||
|
Slides |
The pattern is
created by sliding the shape across the page |
||
|
Flips |
The pattern is created
by flipping the shape |
||
|
Turns |
The pattern is
created by turning the shape |
||
|
Enlarge/Reduce |
The pattern is
created by changing the size |
||
|
|
|
|
|
Appendix 6.4.2
Learn to Draw Course
|
|
Drawing: Using the segment tool, click on point 1and
drag to point 2. Release. Click and drag to point 3. Release. Click and drag
back to point 1. |
Appendix 6.4.3
Transformations
using GSP
Prepare instructions for one transformation (slide, flip, turns, or dilatations) at each computer station.
|
Construct these
shapes on GSP and align them vertically near the left side of the
screen
|
|
To construct Slides: Draw a line using the segment tool below and to the right of the shapes. 1. Holding the shift key down, select the left then right endpoint of the line. 2. Under Transform: Select Mark Vector. Select the shape above the line. 3. Under Transform: Select Translate. Click OK. 4. Repeat with the remaining shapes. 5. Choose one shape: draw a line that points downward to the right and slide the shape. 6. Make your own shape and use what you have learned to slide it. |
|
To construct Flips: Draw a line using the segment tool to the right of each of the shapes. 1. Select the line to the right of a shape. Under Transform: Select Mark Mirror. Select the shape. 2. Under Transform: Select Reflect. 3. Choose one shape: draw a line underneath it and flip the shape. 4. Make your own shape. Use what you have learned to flip it. |
|
Turns: Draw a point to the right of each shape. 1. Select the point to the right of the shape. Under Transform: Select Mark Centre. 2. Select the shape. Under Transform Select Rotate. (Choose 90 degrees). Repeat two times. 3. Drag the point to the left until it touches the shape. What do you notice? 4. Repeat using a different angle (45 -90 or -45 degrees). 5. Make your own shape. Use what you have learned to rotate it. |
|
Dilatation: Draw a point the left of the shape. 1. Select the point to the left of the shape. Under Transform: Select Mark Centre. 2. Select the shape. Under Transform Select Dilate. (Choose 1.5). 3. Drag the point to the left until the shapes sit side by side then drag it to the centre of the shape. 4. Repeat with the rest of the shapes. 5. Make your own shape and reduce it 3 times by selecting 0.75, 0.5 and 0.25 for the scale factor. |
Appendix 6.4.4
Logo
Print and laminate
the Logo on the left and install the “hint” on GSP.
|
|
|
Appendix 6.5.1 – Rubric for Transformations
|
Criteria |
Level 1 |
Level 2 |
Level 3 |
Level 4 |
|
Knowledge/
Understanding |
- demonstrates
limited Understanding of using the Transform menu to create shapes |
- demonstrates
some understanding of using the Transform menu to create shapes |
- demonstrates a
considerable understanding of using the Transform menu to create shapes |
- demonstrates a
thorough understanding of using the transform menu to create shapes |
|
Application |
- uses selection
and arrangement of the symmetry tools with limited effectiveness |
- uses
inconsistent selection and arrangement of the symmetry tools according to an
overall plan with some effectiveness |
- makes selection
and arrangement of the symmetry tools co-ordinating a variety of ideas under
an overall plan |
- makes selection
and arrangement of the symmetry tools according to a sophisticated design
plan |
|
Communication |
- rarely uses
mathematical words correctly applied to describe the transformations |
- sometimes uses
or applies mathematical words correctly to describe the transformations |
- regularly uses
appropriate mathematical words to describe the transformations |
- consistently
uses appropriate mathematical words to describe the transformations |
Note: A student whose achievement is below Level 1
(50%) has not met the expectations for this assignment or activity.
Appendix 6.6.1 – Tiling Instructions
GSP Instructions for shapes in List One1. Select and copy the shape that matches the template used for the paper-and-pencil tiling. Paste the shape in the lower left corner of a new sketch. Make 4 copies. Colour the interior. 2. Select and drag one shape next to another until it meets edge to edge. 3. Repeat with the remaining copies. Copy/Paste large sections to complete the design. Save often. |
GSP Instructions for Shapes in List Two1. Select and copy the shape that matches the template used for the paper and pencil tiling. Paste the shape in the lower left corner of a new sketch. Make 4 copies. Colour the interior. 2. First, on one shape select one point. Under Transform, choose Mark Centre. Second, select the shape then choose the Rotate tool (under the selection arrow on the left toolbar). Third, move the pointer towards the point around which you will rotate. When the pointer becomes a horizontal arrow, press and hold the mouse down. Drag the selection around the centre of rotation until it is in the position you want. Release the mouse button. Fourth, change the Rotate tool to the selection arrow and select the shape. Drag the shape into position so it meets edge to edge. 3. Repeat with the remaining copies. Copy/Paste large sections to complete the design. (Save often.) |
Appendix 6.7.1
Rubric for Summative Activity:
Flooring Project
|
Criteria |
Level 1 |
Level 2 |
Level 3 |
Level 4 |
|
Knowledge/
Understanding Construction
of a scale drawing for the floor space |
- limited
knowledge of scale drawing is demonstrated |
- some knowledge
of scale drawing is demonstrated |
- considerable
knowledge of scale drawing is demonstrated |
- thorough
knowledge of scale drawing is demonstrated |
|
Problem Solving
Analysis and
justification of the purchase recommendation Selection and
sequencing of tools required to create a tiling design |
- makes
recommendations with limited justification - selection and
sequencing of tools suggest limited understanding |
- makes reasonable
recommendations and provides some justification - the tools
selected are appropriate for some of the tiles or sequenced sometimes |
- makes
appropriate recommendations and provides considerable justification - the tools
selected are appropriate and correctly sequenced most of the time |
- make appropriate
recommendations and provides thorough justification - the tools
selected are appropriate and are correctly sequenced all or almost all of the
time |
|
Application Use of the
spreadsheet to calculate and evaluate project costs Make appropriate
purchase recommendations |
- spreadsheet
calculations had limited use for calculating costs - purchase
recommendation has limited validity |
- spreadsheet
calculations lead to some use for calculating costs - purchase
recommendation has some validity |
- spreadsheet
calculations consider most options - purchase
recommendation has a considerable validity |
- spreadsheet
calculations are complete and evaluated within the context of the problem - lead to a high
quality recommendation |
|
Communication Degree of clarity
in the arguments behind their purchase recommendation |
- provides
arguments with limited clarity |
- provides
arguments with some clarity |
- provides
arguments with considerable clarity |
- provides
arguments with high degree of clarity that are fully justified |
Note: A student whose achievement is below Level 1
(50%) has not met the expectations for this assignment or activity.
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